Learning a data-dependent kernel function for KPCA-based nonlinear process monitoring

Kernel principal component analysis (KPCA)-based process monitoring methods have recently shown to be very effective for monitoring nonlinear processes. However, their performances largely depend on the kernel function and currently there is no general rule for kernel selection. Existing methods simply choose the kernel function empirically or experimentally from a given set of candidates. This paper proposes a kernel function learning method for KPCA to learn a kernel function tailored to specific data and explores its potential for KPCA-based process monitoring. Motivated by the manifold learning method maximum variance unfolding (MVU), we obtain the kernel function by optimizing over a family of data-dependent kernels such that the nonlinear structure in input data is unfolded in the kernel feature space and gets more likely to be linear there. Using the optimized kernel, the nonlinear principal components of KPCA which are linear principal components in the kernel feature space can effectively capture the variation in data, and thus the data under normal operating conditions can be more precisely modeled by KPCA for process monitoring. Simulation results on an simple nonlinear system and the benchmark Tennessee Eastman (TE) demonstrate that the optimized kernel functions lead to significant improvement in the performance over the popular Gaussian kernels when used in the KPCA-based process monitoring.     

基于多向核熵成分分析的微生物发酵过程多阶段划分及故障监测

针对多向核主元分析法(MKPCA)在监控动态非线性和多模态间歇生产过程故障的不足,提出一种基于物理信息熵的多阶段多向核熵成分分析(multiple sub-stage multi-way kernel entropy component analysis,MSMKECA)的新方法用于故障监控。该方法首先通过核映射将数据从低维空间映射到高维特征空间;其次在高维特征空间依据熵结构信息计算每个时刻数据矩阵的相似度指标进行阶段划分,将间歇过程划分为各稳定阶段和各过渡阶段,并在过渡阶段用时变的协方差代替固定协方差;最后在划分的阶段里分别建立模型进行间歇过程监测解决间歇过程的动态非线性和多阶段特性;将所提出的算法应用于青霉素发酵仿真系统的在线监测,验证了该方法的有效性。     

基于MKECA的非高斯性和非线性共存的间歇过程监测

多向核独立成分分析（multiway kernel independent component analysis,MKICA）在监测间歇过程非高斯性和非线性方面取得了广泛应用,其仅仅是将线性独立成分分析（independent component analysis,ICA）方法利用核主成分分析（kernel principal component analysis,KPCA）白化扩展到非线性领域,但数据经KPCA白化后只考虑数据信息最大化未考虑数据簇结构信息的不足,为解决此问题,采用核熵成分分析（kernel entropy component analysis,KECA）代替KPCA白化的过程监测方法。该方法首先利用AT展开方法将过程三维数据变为二维数据;其次用KECA进行白化处理的同时解决数据的非线性;然后建立ICA监测模型用于非高斯生产过程监测;最后将该方法应用到青霉素发酵仿真和实际的工业过程并与MKICA方法进行对比,验证该方法的有效性。     

Enhanced statistical analysis of nonlinear processes using KPCA, KICA and SVM

In this paper, some drawbacks of original kernel independent component analysis (KICA) and support vector machine (SVM) algorithms are analyzed for the purpose of multivariate statistical process monitoring (MSPM). When the measured variables follow non-Gaussian distribution, KICA provides more meaningful knowledge by extracting higher-order statistics compared with PCA and kernel principal component analysis (KPCA). However, in real industrial processes, process variables are complex and are not absolutely Gaussian or non-Gaussian distributed. Any single technique is not sufficient to extract the hidden information. Hence, both KICA (non-Gaussion part) and KPCA (Gaussion part) are used for fault detection in this paper, which combine the advantages of KPCA and KICA to develop a nonlinear dynamic approach to detect fault online compared to other nonlinear approaches. Because SVM is available for classifying faults, it is used to diagnose fault in this paper.For above mentioned kernel methods, the calculation of eigenvectors and support vectors will be time consuming when the sample number becomes large. Hence, some dissimilar data are analyzed in the input and feature space.The proposed approach is applied to the fault detection and diagnosis in the Tennessee Eastman process. Application of the proposed approach indicates that proposed method effectively captures the nonlinear dynamics in the process variables.     

基于KPLS模型的间歇过程产品质量控制

针对间歇过程所具有的非线性特性,提出了一种基于核偏最小二乘(KPLS)模型的最终产品质量控制策略。利用初始条件、批次展开后的过程数据以及最终产品质量建立了间歇过程的KPLS模型;采用基于主成分分析(PCA)映射的预估方法对未知的过程数据进行补充,实现了最终产品质量的在线预测。为了解决最终产品质量的控制,利用T2统计量确定KPLS模型的适用范围,并作为约束引入产品质量控制问题,提高控制策略的可行性;采用粒子群优化(PSO)算法实现了优化问题的高效求解。仿真结果表明,与基于偏最小二乘(PLS)模型的控制策略相比,所提出的方法具有更高的预测精度,且能有效解决产品质量控制中出现的各种问题。     

基于核熵独立成分分析的故障检测方法

传统核独立成分分析(KICA)依据特征值的大小进行降维,但是特征值大并不一定取得的信息熵贡献度也是最大的。针对这个问题,提出一种基于核熵独立成分分析(KEICA)的故障检测方法。将训练数据集投影在高维核空间,通过对数据信息熵的贡献大小选取核主成分,并建立独立成分分析(ICA)模型。对训练样本求I²和SPE统计量,并利用核密度估计计算统计量的控制限。计算测试数据对训练数据的核矩阵,将其投影在ICA模型上并计算测试样本的统计量,统计量超出控制限的样本即可被识别为故障样本。将该方法用于非线性数值例子和Tennessee Eastman (TE)过程的故障检测,并与传统的核主成分分析(KPCA)、核熵成分分析(KECA)和KICA方法进行对比,表明KEICA的监测效果优于其他三种方法。     

基于核熵独立成分分析的故障检测方法

传统核独立成分分析（KICA）依据特征值的大小进行降维,但是特征值大并不一定取得的信息熵贡献度也是最大的。针对这个问题,提出一种基于核熵独立成分分析（KEICA）的故障检测方法。将训练数据集投影在高维核空间,通过对数据信息熵的贡献大小选取核主成分,并建立独立成分分析（ICA）模型。对训练样本求和统计量,并利用核密度估计计算统计量的控制限。计算测试数据对训练数据的核矩阵,将其投影在ICA模型上并计算测试样本的统计量,统计量超出控制限的样本即可被识别为故障样本。将该方法用于非线性数值例子和Tennessee Eastman（TE）过程的故障检测,并与传统的核主成分分析（KPCA）、核熵成分分析（KECA）和KICA方法进行对比,表明KEICA的监测效果优于其他三种方法。     

Improved multi-scale kernel principal component analysis and its application for fault detection

In this paper the multiscale kernel principal component analysis (MSKPCA) based on sliding median filter (SFM) is proposed for fault detection in nonlinear system with outliers. The MSKPCA based on SFM (SFM-MSKPCA) algorithm is first proposed and applied to process monitoring. The advantages of SFM-MSKPCA are: (1) the dynamical multiscale monitoring method is proposed which combining the Kronecker production, the wavelet decomposition technique, the sliding median filter technique and KPCA. The Kronecker production is first used to build the dynamical model; (2) there are more disturbances and noises in dynamical processes compared to static processes. The sliding median filter technique is used to remove the disturbances and noises; (3) SFM-MSKPCA gives nonlinear dynamic interpretation compared to MSPCA; (4) by decomposing the original data into multiple scales, SFM-MSKPCA analyze the dynamical data at different scales, reconstruct scales contained important information by IDWT, eliminate the effects of the noises in the original data compared to kernel principal component analysis (KPCA). To demonstrate the feasibility of the SFM-MSKPCA method, its process monitoring abilities are tested by simulation examples, and compared with the monitoring abilities of the KPCA and MSPCA method on the quantitative basis. The fault detection results and the comparison show the superiority of SFM-MSKPCA in fault detection.     

基于辅助变量KNN分析的软测量建模方法

提出一种基于辅助变量最近邻（KNN）分析的软测量建模方法,该方法将KNN算法应用于辅助变量分类,根据分类结果,应用核主成分分析（KPCA）和支持向量回归机（SVR）相结合进行软测量建模。KNN分析独立于后继回归模型,却又直接影响模型结构,KPCA作为中间层,在KNN分类结果指导下提取不同类别包含辅助变量高阶信息的特征主元,然后使用SVR建立特征主元和主导变量之间的回归模型。用该方法建立粗汽油干点软测量模型,结果表明KNN-KPCA-SVR（KKS）模型的预测精度和泛化能力优于线性PLS、RBF核函数SVR和KPCA-SVM模型。     

基于稀疏核主元分析的在线非线性过程监控

核主元分析(KPCA)适合非线性过程的监控,但存在计算量大、实时性差等缺点。提出一种基于稀疏KPCA(SKPCA)的过程监控方法,先使用SKPCA对正常建模数据进行加权,少数权值大的数据基本能代表全部正常数据的信息,因此稀化了建模数据,然后根据稀化后的正常数据建立过程的KPCA模型,并提出监控指标,大大减少了计算量,提高了监控的实时性,最后以化工分离过程为对象,就KPCA与SKPCA的监控效果和实时性进行了详细的对比研究,结果表明了基于SKPCA监控方法的优越性。     

Nonlinear multiscale modelling for fault detection and identification

In order to detect abnormal events at different scales, a number of multiscale multivariate statistical process control (MSPC) approaches which combine a multivariate linear projection model with multiresolution analysis have been suggested. In this paper, a new nonlinear multiscale-MSPC method is proposed to address multivariate process performance monitoring and in particular fault diagnostics in nonlinear processes. A kernel principal component analysis (KPCA) model, which not only captures nonlinear relationships between variables but also reduces the dimensionality of the data, is built with the reconstructed data obtained by performing wavelet transform and inverse wavelet transform sequentially on measured data. A guideline is given for both off-line and on-line implementations of the approach. Two monitoring statistics used in multiscale KPCA-based process monitoring are used for fault detection. Furthermore, variable contributions to monitoring statistics are also derived by calculating the derivative of the monitoring statistics with respect to the variables. An intensive simulation study on a continuous stirred tank reactor process and a comparison of the proposed approach with several existing methods in terms of false alarm rate, missed alarm rate and detection delay, demonstrate that the proposed method for detecting and identifying faults outperforms current approaches.     

核主成分分析-广义回归神经网络法研究——70种烷烃类有机化合物的气相色谱保留指数

利用核主成分分析法和广义回归神经网络研究了70种烷烃在固定相为角鲨烷,柱温50℃时的气相色谱保留指数。核主成分分析将70×8维的样品集降为51×3维,以减少计算量;降维后的样品集作为广义回归神经网络的训练集对色谱保留时间进行计算和预测。该方法的计算结果满足误差要求。     

基于核主角的故障检测方法

基于主元分析（PCA）的统计检测方法已经被广泛应用于各种化工过程的故障检测和识别.移动主元分析（moving principal component analysis,简称MPCA）算法基于PCA,根据主元子空间的变化来判断故障是否发生.然而,基于主元分析的统计检测方法是线性方法,无法有效应用于非线性系统.因此,提出一种适合于非线性系统的故障检测方法——基于核主角(kernel principal angle,简称KPA)的故障检测方法,其基本思想与MPCA相似,主要内容包括构建特征子空间和核主角测量两部分.TE过程故障检测仿真实验证明,基于核主角的故障检测方法优于传统的多元统计检测方法（cMSPC）和MPCA.     

Multivariate time delay analysis based local KPCA fault prognosis approach for nonlinear processes☆

Currently, some fault prognosis technology occasionally has relatively unsatisfied performance especially for in-cipient faults in nonlinear processes duo to their large time delay and complex internal connection. To overcome this deficiency, multivariate time delay analysis is incorporated into the high sensitive local kernel principal com-ponent analysis. In this approach, mutual information estimation and Bayesian information criterion (BIC) are separately used to acquire the correlation degree and time delay of the process variables. Moreover, in order to achieve prediction, time series prediction by back propagation (BP) network is applied whose input is multivar-iate correlated time series other than the original time series. Then the multivariate time delayed series and future values obtained by time series prediction are combined to construct the input of local kernel principal component analysis (LKPCA) model for incipient fault prognosis. The new method has been exemplified in a sim-ple nonlinear process and the complicated Tennessee Eastman (TE) benchmark process. The results indicate that the new method has superiority in the fault prognosis sensitivity over other traditional fault prognosis methods. ? 2016 The Chemical Industry and Engineering Society of China, and Chemical Industry Press. Al rights reserved.     

Multivariate statistical monitoring of the aluminium smelting process

This paper describes the development of a new ‘cascade’ monitoring system for the aluminium smelting process that uses latent variable models. This system is based on the changes of variability patterns within a feeding cycle which are used to provide indications of faults and their possible causes. The system has been tested offline using 31 data sets. The performance of the system to detect an anode effect has been compared with a typical latent variable model that monitors the change of behaviour at every time instant. The results show that the ‘cascade’ monitoring system is able to detect abnormal events. It was possible to relate each event with specific patterns associated with abnormalities thus facilitating later fault diagnosis.     

基于主元独立性分析与混合核RVM的复杂过程区间预测方法研究及应用

近年来,随着化工过程日趋复杂,对过程监控及关键变量预测提出了更高的要求。传统意义上的点预测已不能满足化工过程上的实际需求,且点预测无法描述过程上的不确定性问题,因此不能很好地把握预测变量的趋势。由此,提出了一种基于主元独立性分析（principal component independent analysis,PCIA）与混合核相关向量机（RVM）的区间预测方法。首先,结合核主元成分分析（KPCA）和独立元分析（ICA）对复杂过程原始变量进行主元成分提取和独立性分析,形成独立主元;其次,将高斯核函数与多项式核函数相结合形成混合核,与RVM结合对得到的独立主元进行回归建模预测,并运用T分布对预测值进行区间估计;然后,构造区间评价综合函数对区间估计结果进行优劣分析,在分析预测区间覆盖率（PICP）及预测区间宽度（NMPIW）的基础上,引入累积偏差（AD）提高区间评判的合理性。最后,将所提方法应用到TE仿真过程进行区间预测分析,仿真结果表明,提出的区间预测方法对实际生产过程具有较高的预测精度和区间估计质量,可以有效地预测关键变量的趋势。